A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. including part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Conventional lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at once, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti-parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
A lithographic apparatus usually comprises one or more objects that need to be accurately positioned such as a support constructed to support the patterning device and/or a substrate table constructed to hold a substrate. The lithographic apparatus therefore generally comprises an object positioning system for positioning the object, wherein the object positioning system comprises: a measurement system with one or more sensors for measuring the position of the object in one or more degrees of freedom relative to a reference; an actuator system with one or more actuators for positioning the object; and a control system configured to drive the actuator system in dependency of an output of the measurement system and a set point representing a desired position of the object.
With the increasing demand for higher throughput, the accelerations applied to the object also increase. This will result in excitation of internal dynamical modes of the object, such as a torsion mode and an umbrella mode. When the internal dynamical modes are relatively low-frequency and are observable by the measurement system, they may limit the obtainable bandwidth of the closed-loop object positioning system and thus limit the performance, i.e. speed and accuracy, of the object positioning system.
Another drawback is that depending on the type of measurement system, the internal dynamics may be observed differently by the measurement system for different positions of the object. Control design is therefore based on worst-case scenarios in order to be robust for all positions of the object which limits the obtainable bandwidth even further.